For the extreme implementation without any sensing elements mounted on the IRS, the IRS becomes fully passive [1]}, [2]}. Due to the deficiency of baseband signal processing capability, the IRS can no longer estimate the BS-IRS link and the user-IRS link separately. Instead, some recent research endeavour to estimate the cascaded reflection channels, which is the Khatri-Rao product of the BS-IRS link and the user-IRS link [3]}, [4]}. Along this line of thought, the most straightforward method is to estimate the direct and cascaded reflection channels in sequence upon switching on only a single element at each time slot, and thus the direct channel and reflection channels can be estimated separately without mutual interference [5]}. However, it is obvious to note that the ON/OFF method suffers from severe power loss due to the frequent switching off the IRS. To solve this problem, [6]} proposed a novel channel estimation method by designing orthogonal IRS reflection coefficient vector during the channel estimation phase, thus the cascaded reflection channels can be obtained without the power loss as well as the mutual interference. In addition, [7]} noted that the reflection channels associated with different users share the common BS-IRS link, and then proposed a novel three-phase channel estimation method, which estimates a set of low-dimensional scaling factors instead of directly estimating reflection channel coefficients. Furthermore, the authors of [8]} reduced the pilot overhead by arranging the IRS elements into groups and estimating only a single channel coefficient for each group, which suffers from the performance penalty. Recently, several new research results have been reported by reducing the dependency of the IRS reflection optimization on accurate CSI. In [9]}, the statistic CSI is exploited to perform the phase shift optimization at the expense of system performance. Our prior work has demonstrated that multiple independent random phase shifts can gradually approach the optimal performance, where only the effective sum channel is estimated instead of separately estimating the direct channel and reflection channels [10]}. The interested reader may refer to [3]}, [12]}, [13]} and references therein to find the most state-of-the-art channel estimation methods for IRS-assisted wireless systems.
